def fitLine(points, c='orange', lw=1, alpha=0.6, legend=None):
'''
Fits a line through points.
Extra info is stored in actor.slope, actor.center, actor.variances
[**Example**](https://github.com/marcomusy/vtkplotter/blob/master/examples/basic/fitline.py)
'''
data = np.array(points)
datamean = data.mean(axis=0)
uu, dd, vv = np.linalg.svd(data - datamean)
vv = vv[0]/np.linalg.norm(vv[0])
# vv contains the first principal component, i.e. the direction
# vector of the best fit line in the least squares sense.
xyz_min = points.min(axis=0)
xyz_max = points.max(axis=0)
a = np.linalg.norm(xyz_min - datamean)
b = np.linalg.norm(xyz_max - datamean)
p1 = datamean - a*vv
p2 = datamean + b*vv
l = vs.line(p1, p2, c=c, lw=lw, alpha=alpha)
l.info['slope'] = vv
l.info['center'] = datamean
l.info['variances'] = dd
return l
def fitLine(points, c='orange', lw=1, alpha=0.6, legend=None):
'''
Fits a line through points.
Extra info is stored in actor.slope, actor.center, actor.variances
'''
data = np.array(points)
datamean = data.mean(axis=0)
uu, dd, vv = np.linalg.svd(data - datamean)
vv = vv[0] / np.linalg.norm(vv[0])
# vv contains the first principal component, i.e. the direction
# vector of the best fit line in the least squares sense.
xyz_min = points.min(axis=0)
xyz_max = points.max(axis=0)
a = np.linalg.norm(xyz_min - datamean)
b = np.linalg.norm(xyz_max - datamean)
p1 = datamean - a * vv
p2 = datamean + b * vv
l = vs.line(p1, p2, c=c, lw=lw, alpha=alpha)
setattr(l, 'slope', vv)
setattr(l, 'center', datamean)
setattr(l, 'variances', dd)
return l
return 1j*(nabla2psi - V*psi) # this is the RH of Schroedinger equation!
def d_dt(psi): # find Psi(t+dt)-Psi(t) /dt with 4th order Runge-Kutta method
k1 = f(psi)
k2 = f(psi +dt/2*k1)
k3 = f(psi +dt/2*k2)
k4 = f(psi +dt *k3)
return (k1 + 2*k2 + 2*k3 + k4)/6
vp = Plotter(interactive=0, axes=2, verbose=0, bg=(0.95,0.95,1))
vp.xtitle = ''
vp.ytitle = 'Psi^2(x,t)'
vp.ztitle = ''
bck = vp.load('data/images/schrod.png', alpha=.3).scale(.0255).pos([0,-5,-.1])
barrier = shapes.line(list(zip(x, V*15, [0]*len(x))), c='black', lw=2)
lines = []
for i in range(0, Nsteps):
for j in range(500):
Psi += d_dt(Psi) * dt # integrate for a while before showing things
A = np.real( Psi*np.conj(Psi) )*1.5 # psi squared, probability(x)
coords = list(zip(x, A, [0]*len(x)))
Aline = shapes.line(coords, c='db', lw=3)
vp.show([Aline, barrier, bck])
lines.append([Aline, A]) # store objects
# now show the same lines along z representing time
vp.clear()
vp.camera.Elevation(20)
vp.camera.Azimuth(20)